"34 Art. 4.— M. Kuniyeda : 



{E) : /;, I,, , >^,„ (lim/„ = oo), 



such that, for every À„, we liave 



all values of ;. iu (U) being greater than a certain positive number 

 A which can be determined corresponding to each given P. 



Since ^ = y > 1 as ; tends to infinity, taking the values of 

 the sequence (^\ we can always choose a number a such that 



1 < a < /^ < dja. 



Easily we can see that H-lernma 24 is available in our case. 

 Hence we have 



/W=m/-^)</(^,) (f>^l 



Therefore, by (33), we have 



or 



(34) 



\-^f{-^){^+^)<cK {f<\). 



But rj>P, --y/(:y) >//-*> P- 



-i 



and the value of P may be chosen as large as we please. Hence 

 neither of the inequalities of (34) can be true. 



Thus ^ cannot take values which become indefinitely great 

 as )^-^a:> . 



Next, if we suppose that 3y<l, or f] oscillates in such a manner 

 that it takes indefinitely small values as /'>->x, then, corresponding 

 to any prescribed positive number p, however small, there will 

 exist a sequence {E) of values of )~ tending to infinity such tliat, 

 for every value of / of this sequence, we have 



